A Novel Approximation to Dynamic Time Warping allows Anytime Clustering of Massive Time Series Datasets

Given the ubiquity of time series data, the data mining community has spent significant time investigating the best time series similarity measure to use for various tasks and domains. After more than a decade of extensive efforts, there is increasing evidence that Dynamic Time Warping (DTW) is very difficult to beat. Given that, recent efforts have focused on making the intrinsically slow DTW algorithm faster. For the similarity-search task, an important subroutine in many data mining algorithms, significant progress has been made by replacing the vast majority of expensive DTW calculations with cheap-to-compute lower bound calculations. However, these lower bound based optimizations do not directly apply to clustering, and thus for some realistic problems, clustering with DTW can take days or weeks. In this work, we show that we can mitigate this untenable lethargy by casting DTW clustering as an anytime algorithm. At the heart of our algorithm is a novel data-adaptive approximation to DTW which can be quickly computed, and which produces approximations to DTW that are much better than the best currently known linear-time approximations. We demonstrate our ideas on real world problems showing that we can get virtually all the accuracy of a batch DTW clustering algorithm in a fraction of the time.